Sister chromatid cohesion, crucial for faithful segregation of replicated chromosomes in eukaryotes, is mediated by the multi-subunit protein complex cohesin. The Saccharomyces cerevisiae plasmid 2 micron circle mimics chromosomes in assembling cohesin at its partitioning locus. The plasmid is a multi-copy selfish DNA element that resides in the nucleus and propagates itself stably, presumably with assistance from cohesin. In metaphase cell lysates, or fractions enriched for their cohesed state by sedimentation, plasmid molecules are trapped topologically by the protein ring formed by cohesin. They can be released from cohesin's embrace either by linearizing the DNA or by cleaving a cohesin subunit. Assays using two distinctly tagged cohesin molecules argue against the hand-cuff (an associated pair of monomeric cohesin rings) or the bracelet (a dimeric cohesin ring) model as responsible for establishing plasmid cohesion. Our cumulative results most easily fit a model in which a single monomeric cohesin ring, rather than a series of such rings, conjoins a pair of sister plasmids. These features of plasmid cohesion account for its sister-to-sister mode of segregation by cohesin disassembly during anaphase. The mechanistic similarities of cohesion between mini-chromosome sisters and 2 micron plasmid sisters suggest a potential kinship between the plasmid partitioning locus and centromeres.